Opposite angles of a parallelogram are congruent.
a. True
b. False
Which geometric series converges?
A. 2+0.2+0.02+0.002+...
B. 2+4+8+16+...
C. 2-20+200-2000+...
D. 2+2+2+2+...
Answer: The correct option is (A) 2 + 0.2 + 0.02 + 0.002 + . . .
Step-by-step explanation: We are given to select the correct geometric series that converges.
We know that
a geometric series converges if the modulus of its common ratio is less than 1.
Option (A) : 2 + 0.2 + 0.02 + 0.002 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{0.2}{2}=\dfrac{0.02}{0.2}=\dfrac{0.002}{0.02}=~.~.~.~=0.1\\\\\Rightarrow |r|=|0.1|=0.1<1[/tex]
So, this geometric series will converge.
Option (A) is correct.
Option (B) : 2 + 4 + 8 + 16 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{4}{2}=\dfrac{8}{4}=\dfrac{16}{8}=~.~.~.~=2\\\\\Rightarrow |r|=|2|=2>1.[/tex]
So, this geometric series will not converge.
Option (B) is incorrect.
Option (C) : 2 - 20 + 200 - 2000 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{-20}{2}=\dfrac{200}{-20}=\dfrac{-2000}{200}=~.~.~.~=-10\\\\\Rightarrow |r|=|-10|=10>1.[/tex]
So, this geometric series will not converge.
Option (C) is incorrect.
Option (D) : 2 +2 + 2 + 2 + . . .
Here, first term, a= 2 and the common ratio is given by
[tex]r=\dfrac{2}{2}=\dfrac{2}{2}=\dfrac{2}{2}=~.~.~.~=1\\\\\Rightarrow |r|=|1|=1.[/tex]
So, this geometric series will not converge.
Option (D) is incorrect.
Thus, the correct option is (A).
The geometric series that converges is 2+0.2+0.02+0.002+ ...:
Thus, option (A) is correct.
In a geometric series, the terms are multiplied by a constant ratio to obtain the next term.
If the absolute value of the common ratio is less than 1, the series converges.
A. 2 + 0.2 + 0.02 + 0.002 + ...:
In this series, the common ratio is 0.1 (each term is divided by 10).
Since the absolute value of the common ratio is less than 1, this series converges.
B. 2 + 4 + 8 + 16 + ...:
In this series, the common ratio is 2 (each term is multiplied by 2).
Since the common ratio is greater than 1, this series diverges.
C. 2 - 20 + 200 - 2000 + ...:
In this series, the terms alternate in sign, but the absolute value of the common ratio is 10.
Since the absolute value of the common ratio is greater than 1, this series diverges.
D. 2 + 2 + 2 + 2 + ...:
In this series, the common ratio is 1 (each term is the same).
Since the common ratio is equal to 1, this series neither converges nor diverges. It is a divergent series.
Therefore, the geometric series that converges is 2 + 0.2 + 0.02 + 0.002 + ...
Thus, option (A) is correct.
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A rectangle that has an area of 357 square inches is 17 inches wide. How long is the rectangle?
If a fair coin is tossed 9 times, in how many different ways can the sequence of heads and tails appear
Angle C is an inscribed angle of circle P. Angle C measures (3x + 5)° and arc AB measures (16x)°. Find x.
Final answer:
By applying the theorem that an inscribed angle is half the measure of its intercepted arc, we can solve the given equation to find that the value of x is 1.
Explanation:
The problem involves the relationship between an inscribed angle and its intercepted arc in a circle, which is a fundamental concept in circle geometry. According to the theorem that states an inscribed angle is half the measure of its intercepted arc, we can set up an equation to find the variable x.
Given that angle C measures (3x + 5)° and arc AB measures (16x)°, the relationship between them can be expressed as:
Angle C = ½ × measure of arc AB
(3x + 5)° = ½ × (16x)°
Solving this equation for x gives:
3x + 5 = 8x
5 = 5x
x = 1
Therefore, the value of x is 1.
An object is thrown upward with an initial velocity of 32 feet per second. The objects height is modeled by the function h(t) = - 16t2 + 32t where t is the time of the at height, h(t). What is the maximum height of the object?
32 ft
60 ft
72 ft
104 ft
verify the identity
cosx/1+sinx + 1+sin/cosx = 2sec x
PLEASE HELP!!!!! The velocity of sound in air is given by the equation , where v is the velocity in meters per second and t is the temperature in degrees Celsius. Find the temperature when the velocity is 329 meters per second by graphing the equation. Round the answer to the nearest degree. Show your work.
The equation of velocity of sound in air is v = 20 √(273 + t). In this problem, we need to find the temperature when the velocity is 329 meters/s. You need to measure the time it takes a sound to travel a measured distance in order to measure its speed in air.
Given:
Velocity of sound in air equation = v = 20 √(273 + t)
Velocity = 329 m/s
To solve:
V = 20 √(273 + t)
329 = 20 * sqrt(273 + t)
16.45 = sqrt(273 + t)
273 + t = 16.45^2
t- 16.45^2-273
t = -2.4 degrees Celsius
So, the temperature when the velocity is 329 meters per second is -2.4 degrees Celsius.
A certain drug dosage calls for 25 mg per kg per day and is divided into two doses (1 every 12 hours). if a person weighs 80 pounds, how much of the drug should be administered each time?
The required amount of drug for each time a day is given as 425 mg.
What is a Measurement unit?A measurement unit is a unit to measure certain quantities.
For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.
To find the measurement of a new quantity known units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.
Given that,
The weight of the person is 80 pounds.
The amount of dose of drug per day is 25 mg/kg
Then, the amount of drug for each time a day is 12.5 mg/kg.
The weight of the person in kilogram can be calculated as follows,
1 pound = 0.45 kg
Then, 80 pounds = 0.45 × 80
= 34 kg
Now, the amount of drug to be taken each time is 34 × 12.5 = 425mg.
Hence, the amount of drug that should be administered to the person each time is 425 mg.
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P, Q, and R are three different points. PQ = 3x + 2, QR = x, RP = x + 2, and . List the angles of PQR in order from largest to smallest and justify your response.
The angles of triangle PQR are ordered from largest to smallest as <>R,
The question involves applying the principles of geometry to compare lengths of sides in a triangle, and thereby determine the relative magnitude of angles in triangle PQR. According to the triangle inequality theorem, the largest angle in a triangle is opposite the longest side, and the smallest angle is opposite the shortest side. Given that the side lengths are represented as PQ = 3x + 2, QR = x, and RP = x + 2, we can compare the expressions to conclude which side is longest and which is shortest, assuming all values of x are positive since they represent lengths.
Firstly, it is obvious that QR (x) is the shortest side since it is just x without any additional positive value. Secondly, between RP (x + 2) and PQ (3x + 2), PQ will always be longer than RP for all positive x because it has a larger coefficient in front of x. Hence, the angle opposite PQ (angle R) will be the largest angle, and the angle opposite QR (angle P) will be the smallest. The angle at Q will be between the other two angles in terms of their measurements since PQ is longer than RP but both are longer than QR.
To summarize, the angles of Triangle PQR ordered from largest to smallest are: ∠R, ∠Q, and ∠P.
The linear equation when b = 5 and m = –2 is
Answer:
y=-2x+5
Step-by-step explanation:
Which function below is the inverse of f(x) = The quantity of four x minus three, over two.?
A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?
A drawer contains five pairs of socks that are brown, black, white, red, and blue. Claude takes the red socks out of the drawer. What is the probability of Claude choosing the red socks on his first pick?
Answer: 1/25
Answer:
The answer would be 1/25 Hopefully this any T4L students!
PLEASE HELP precal!
The expression 9n is also considered a _____.
constant
variable
term
Answer:
Term
Step-by-step explanation:
hope this helps
Which of the following is a solution of x2 + 4x + 10?
2 + i times the square root of 6
−2 + i times the square root of 24
−2 + i times the square root of 6
2 + i times the square root of 24
Answer:
[tex]x=2+-i \sqrt{6}[/tex]
Step-by-step explanation:
[tex]x^2 + 4x + 10[/tex]
To find out the solution we set the expression =0 and solve for x
[tex]x^2 + 4x + 10=0[/tex]
Apply quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=1, b=4, c=10 plug in the values in the formula
[tex]x=\frac{-4+-\sqrt{4^2-4(1)(10)}}{2a}[/tex]
[tex]x=\frac{-4+-\sqrt{-24}}{2(1)}[/tex]
The value of square root (-1) is 'i'
[tex]x=\frac{-4+-2i\sqrt{6}}{2}[/tex]
Divide each term by 2
[tex]x=2+-i\sqrt{6}[/tex]
Is the following relation a function? x y −1 −2 2 3 3 1 6 −2
Answer:
Yes, the relation is a function.
Step-by-step explanation:
We have been given the table
x y
-1 -2
2 3
3 1
6 -2
We know that a relation is a function if every x value has a unique y value.
For the given relation all the x values have a single and unique y values. For example -1 has value -2, 2 has a value 3, 3 has a value 1 and 6 has a value -2.
Thus, the given relation is a function.
What is the exact value of x in the exponential equation 15.5 + e10x = 85.5?
Find the base of a parallelogram with an area (
a. of 60 square inches and height (h) of 4 inches. Use the formula for the area of a parallelogram
The base of parallelogram is 15 inches.
What is parallelogram?A parallelogram is a two-pair quadrilateral with parallel sides. A parallelogram has opposite sides that are the same length and have opposite angles that are the same size. Additionally, the interior angles on the same transversal side are supplemental. 360 degrees is the sum of all the interior angles.
Given area of a parallelogram is 60 square inches
area of parallelogram is given by product of base and height,
Area = b × h
where b = base and h = height
height = 4 inches
Area = b × h
60 = b × 4
b = 60/4 = 15 inches
Hence the base is 15 inches.
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Determine whether the equation represents y as a function of x 16x-y^4=0
99 POINTS!!! Find the equation for an ellipse with vertices at (-6, 0) and (6, 0) and foci at (-4, 0) and (4, 0).
(x^2)/a^2+(y^2)/b^2=1
a>b
a=6, a^2=36
foci=(a^2-b^2)^(1/2)
4=(36-b^2)^(1/2)
16=36-b^2
b^2=36-16
b^2=20
b=2(5)^(1/2) or (20)^(1/2)
1=(x^2/36)+(y^2/20)
Tell which equation you would use to isolate a variable in order to solve the system using substitution. Explain your reasoning.
2x + y=-10
3x-y=0
The length of a rectangle is 2 yd longer than its width. if the perimeter of the rectangle is 40 yd , find its area.
perimeter = 2L+2W
L=2+w
40 = 2L+2W
40= 2(2+w)+2W
40=4+2w+2w
36=4w
w=9
L=9+2=11
2(9) = 18, 2(11) = 22, 22+18 = 40
L=11
W=9
Area = L x w
area = 11x9= 99 square yards
Identify intervals on which the function is increasing, decreasing, or constant. g(x) = 4 - (x - 6)^2 ??
Given the arithmetic sequence A1, A2, A3, A4, 58,69,80,91
What is the Value of A21?
***PLEASE HELP******
Assume that y varies inversely with x. If y=7 when x=2/3, find y when x=7/3
Barry’s Bagel Emporium sells a dozen bagels for $5.00. This price is no longer high enough to create a profit. The owner decides to raise the price. He does not want to alarm his customers with too large of an increase. He is considering four different plans. Plan A: Raise the price by $0.05 each week until the price reaches $8.00. Plan B: Raise the price by 10 percent each week until the price reaches $8.00. Plan C: Raise the price by the same amount each week for 6 weeks, so that in the sixth week the price is $8.00. Plan D: Raise the price by $0.25 each week until the price reaches $8.00. Which plan will result in the price of the bagels reaching $8.00 fastest? plan A plan B plan C
Answer:
Plan B is correct answer.
Step-by-step explanation:
Raise the price by 10 percent each week until the price reaches $8.00.
Week 1. Starting price $5
[tex]0.1\times5=0.5[/tex]
price becomes = [tex]5+0.5=5.5[/tex]
Week 2.
[tex]0.1\times5.5=0.55[/tex]
Price becomes = [tex]5.5+0.55=6.05[/tex]
Week 3.
[tex]0.1\times6.05=0.605[/tex]
Price become = [tex]6.05+0.605=6.655[/tex]
Week 4.
[tex]0.1\times6.655=0.6655[/tex]
Price becomes = [tex]6.655+0.6655=7.320[/tex]
Week 5.
[tex]0.1\times7.320=0.732[/tex]
Price becomes = [tex]7.320+0.732=8.052[/tex]
So, we can see that in 5 weeks the price becomes $8 from $5. Therefore, plan B is the best plan.
75% of our 1000 products are shipped on time each month the remainder have defects that take two weeks to fix and ship our clients complain about 10% of the anti-products are defective and 5% of the product shipped late or defective what is the overall percentage of defective products
Final answer:
Calculating the overall percentage of defective products from the given data, we find that 150 out of 1000 products are defective, leading to an overall defect rate of 15%.
Explanation:
The question asks us to calculate the overall percentage of defective products based on the given scenarios. Firstly, it's mentioned that 75% of 1000 products are shipped on time, which means 750 are shipped on time and 250 are initially defective.
Since clients complain that 10% of the products are defective and 5% of the products are shipped late or are defective, we need to consider these percentages in our calculations.
To find the number of defective products, we can assume the 10% complaint rate on the entire batch of products which would lead to 100 out of 1000 products being defective. This is the initial estimated number of defective products.
To address the 5% of the products that are both shipped late and are defective, we consider this as an additional defect rate on top of the existing one, which would be another 50 products.
Total defects would then be the sum of defects from the complaints about defects and the defects because of shipping delay, which amounts to 100 + 50 = 150 defective products. To find the overall percentage, we divide 150 by 1000 and multiply by 100, giving us an overall defect rate of 15%.
HONORS PROJECT GEOMETRY HELP
Maurice and Johanna have appreciated the help you have provided them and their company Pythgo-grass. They have decided to let you consult on a big project.
1, A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.
2, An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.
3, There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.
4, A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.
5, Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.
An angle is 15 degrees less than twice its complement. find the angles